6. Normal Distribution and Continuous Random Variables

Find the z-score such that the area to the right of the z-score is 0.483.

"In Problems 5–14, a discrete random variable is given. Assume the probability of the random variable will be approximated using the normal distribution. Describe the area under the normal curve that will be computed. For example, if we wish to compute the probability of finding at least five defective items in a shipment, we would approximate the probability by computing the area under the normal curve to the right of x = 4.5.

The probability that exactly eight defective parts are in the shipment

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Find the value of z₀.₂₀.

The heights of adult women are approximately normally distributed with a mean of $160\mathrm{cm}$ and a standard deviation of $7\mathrm{cm}$. Find the height $x$ such that $5\%$ of women are shorter than $x$.

"In Problems 5–14, a discrete random variable is given. Assume the probability of the random variable will be approximated using the normal distribution. Describe the area under the normal curve that will be computed. For example, if we wish to compute the probability of finding at least five defective items in a shipment, we would approximate the probability by computing the area under the normal curve to the right of x = 4.5.

The probability that the number of people with blood type O-negative is between 18 and 24, inclusive"

In a binomial experiment with n trials and probability of success p, if __ ________, the binomial random variable X is approximately normal with μX = ________ and σX = ________.

[DATA] Homeruns Go to www.pearsonhighered.com/sullivanstats to obtain the data file 12_2_24 using the file format of your choice for the version of the text you are using. The variable “TrueDist” represents the distance, in feet, that the homerun traveled for all homeruns hit in the 2014 season.

f. Use a normal model to determine the first and third quartiles. Compare this result to the quartiles found in part (c).

Explain why P(X < 30) should be reported as < 0.0001 if X is a normal random variable with mean 100 and standard deviation 15.

"Females Living at Home According to the Current Population Survey (Internet release date: September 15, 2004), 46% of females between the ages of 18 and 24 years lived at home in 2003. (Unmarried college students living in a dorm are counted as living at home.) Suppose a survey is administered today to 200 randomly selected females between the ages of 18 and 24 years, and 110 of them respond that they live at home.

a. Approximate the probability that such a survey will result in at least 110 of the respondents living at home under the assumption that the true percentage is 46%."

"In Problems 5–14, a discrete random variable is given. Assume the probability of the random variable will be approximated using the normal distribution. Describe the area under the normal curve that will be computed. For example, if we wish to compute the probability of finding at least five defective items in a shipment, we would approximate the probability by computing the area under the normal curve to the right of x = 4.5.

The probability that more than 20 people want to see the marriage tax penalty abolished"

"In Problems 5–14, a discrete random variable is given. Assume the probability of the random variable will be approximated using the normal distribution. Describe the area under the normal curve that will be computed. For example, if we wish to compute the probability of finding at least five defective items in a shipment, we would approximate the probability by computing the area under the normal curve to the right of x = 4.5.

The probability that at least 40 households have a gas stove"

"Liars According to a USA Today “Snapshot,” 3% of Americans surveyed lie frequently. You conduct a survey of 500 college students and find that 20 of them lie frequently.

a. Compute the probability that, in a random sample of 500 college students, at least 20 lie frequently, assuming the true percentage is 3%."

Give three interpretations for the area under a normal curve.

"In Problems 5–14, a discrete random variable is given. Assume the probability of the random variable will be approximated using the normal distribution. Describe the area under the normal curve that will be computed. For example, if we wish to compute the probability of finding at least five defective items in a shipment, we would approximate the probability by computing the area under the normal curve to the right of x = 4.5.

The probability that no more than 500 adult Americans support a bill proposing to extend daylight savings time

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Suppose X is a binomial random variable. To approximate P(X < 5), compute ________.